NCERT Solutions for Class 7th Maths Chapter 6 Number Play
Updated on 2026-09-19
About this chapter
Numbers can carry information about an arrangement without telling you the actual values — each child calls out how many children ahead of them are taller. Parity means being even or odd. An even number can be arranged in pairs; an odd number always leaves one out. Parity rules: even + even = even, odd + odd = even, even + odd = odd. A sum of an odd count of odd numbers is odd; of an even count of odd numbers is even. The n th even number is 2n and the n th odd number is 2n – 1. In a 3 × 3 grid filled with 1 – 9, all row sums add to 45 and all column sums add to 45. A magic square from 1 – 9 has magic sum 15 and 5 at the centre. The Virahāṅka sequence 1, 2, 3, 5, 8, 13, 21, 34, 55, … was first written down in India around 700 CE while counting rhythms of short and long syllables. In a cryp
- Numbers Tell us Things
- Picking Parity
- Small Squares in Grids
- Parity of Expressions
- Some Explorations in Grids
- Generalising a 3 × 3 Magic Square
- The First-ever 4 × 4 Magic Square
- The Virahāṅka–Fibonacci Numbers
- Digits in Disguise
Quick revision
| Idea | What it means | Rule / formula | Example |
|---|---|---|---|
| Line-up number | How many children ahead of you are taller | Count taller people in front | 0, 0, 1, 0, 3, 0, 3 |
| Parity | Being even or odd | Even = pairs up fully; odd = one left over | 12 is even, 13 is odd |
| Adding evens | Always even | even + even = even | 4 + 8 + 10 = 22 |
| Adding odds | Depends on how many | Even count → even; odd count → odd | 3 + 5 = 8; 3 + 5 + 7 = 15 |
| nth even / odd number | Value at a given position | 2n and 2n – 1 | 100th odd = 200 – 1 = 199 |
| Parity of m × n | Small squares in a grid | Odd only if both m and n are odd | 27 × 13 → odd |
| Row and column sums | Grid filled with 1 – 9 | All three row sums add to 45 | 13 + 14 + 18 = 45 |
| Magic square (1 – 9) | Rows, columns, diagonals equal | Magic sum 15, centre 5 | 8 1 6 / 3 5 7 / 4 9 2 |
| Generalised magic square | Built around the centre m | Magic sum = 3m | Centre 25 → magic sum 75 |
| Virahāṅka numbers | Each term = sum of previous two | 1, 2, 3, 5, 8, 13, 21, 34, … | 8 beats → 34 rhythms |
| Cryptarithm | Letters stand for digits | Same letter = same digit | UT + TA = TAT → 91 + 10 = 101 |
Exercises
- In-text Questions — Numbers Tell us Things Page 127
- In-text Questions — Numbers Tell us Things Page 128
- Figure it Out — Numbers Tell us Things Page 128
- In-text Questions — Picking Parity Page 129
- In-text Questions — Picking Parity Page 130
- Figure it Out — Picking Parity Page 131
- Small Squares in Grids — In-text Questions Page 131
- Parity of Expressions — In-text Questions Page 132
- In-text Questions — Some Explorations in Grids Page 133
- In-text Questions — Some Explorations in Grids Page 134
- In-text Questions — Some Explorations in Grids Page 135
- In-text Questions — Some Explorations in Grids Page 136
- Figure it Out — Some Explorations in Grids Page 136
- Generalising a 3 × 3 Magic Square — Math Talk Page 137
- Generalising a 3 × 3 Magic Square — Figure it Out Page 137
- The First-ever 4 × 4 Magic Square — In-text Questions Page 137
- In-text Questions — Nature’s Favourite Sequence: The Virahāṅka–Fibonacci Numbers! Page 140–141
- In-text Questions — The Virahāṅka–Fibonacci Numbers Page 142
- In-text Questions — Digits in Disguise Page 143
- Figure it Out — Digits in Disguise Page 143–144